Welcome!The Topic For Today Is…

Exponential and Logarithmic EquationsExponentialFunctions

Logarithmic Functions

Expanding Expressions

CondensingExpressions

SolvingEquations

200 200 200 200 200

400 400 400 400 400

600 600 600 600 600

800 800 800 800 800

1000 1000 1000 1000 1000

Exponential Functions: 200

• Question:Evaluate f(x) = 25-3x at x=2/3.

• Answer0.0016 or 1/625

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Exponential Functions: 400

• Question:What is the asymptote of f(x) = 0.3x+1?

• Answery = 0

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Exponential Functions: 600

• Question:Is the function increasing or decreasing?g(x) = 0.3-x

• AnswerDecreasing

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Daily Double

The Winner Of The Last RoundWrite Down How Much Money

You Are Willing To RiskIf You get the Question write you win that money

If you get it wrong you Loss the money!

Exponential Functions: 800

• Question:A car is bought for $24,000. It depreciates at arate of 14.5% per year. What will the value of the car be in 10 years?

• Answer$5010.40

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Exponential Functions: 1000

• Question:There are 3 options for investing $500. The first earns 7.5% compounded annually, the second earns 7.25% compounded quarterly, and the second earns 7% compounded continuously. Determine which investment yields the highest return in 20 years.

• AnswerOption Number 1.

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Logarithmic Functions: 200

• Question:Write as a exponential equation. log381 = 4.

• Answer34 = 81

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Logarithmic Functions: 400

• Question:Solve the equation for x. log662 = x

• Answerx = 2

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Logarithmic Functions: 600

• Question:Describe the relationship between the graphs of f and g.

f(x) = 5x g(x) = log5x• Answer

The graphs are symmetric around the line y = x because f(x) and g(x) are inverse functions.

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Logarithmic Functions: 800

• Question:Find the domain, range, vertical asymptote, and x- and y-intercepts of f(x) = 4 log5(x + 2) - 3

• Answer– Domain: (0, ∞)– Range: (- ∞, ∞)– Vertical Asymptote: x = -2– x – intercept: ( 53/4 - 2, 0)– y – intercept: (0, 4 log52 – 3)

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Logarithmic Functions: 1000

• Question:Graph f(x) = –log2(x - 4) + 5

• AnswerSee the teacher for the answer.

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Expanding Expressions: 200

• Question: Expand the log.ln (z(z + 1)2)

• Answerln z + 2ln(z + 1)

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Expanding Expressions: 400

• Question: Expand the natural log.ln

• Answer

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3xy

1 1ln ln3 3

x y

Expanding Expressions: 600

• Question: Expand the natural log.

• Answerln (x + 1) + ln (x – 1) – 3 ln x

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)1ln( 3

2

xx

Expanding Expressions: 800

• Question: Expand the natural log.

• Answer4 ln x + ln y – 5 ln z

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4

5ln x yz

Expanding Expressions: 1000

• Question: Expand the log.

• Answer

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2

2 3logbxy z

2log 2log 3logb b bx y z

Condensing Expressions: 200

• Question:Condense the logarithm to a single quantity.4[lnz + ln(z + 5)] – 2ln(z – 5)

• Answer

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4 4

2

( 5)ln( 5)z zz

Daily Double

The Winner Of The Last RoundWrite Down How Much Money

You Are Willing To RiskIf You get the Question write you win that money

If you get it wrong you Loss the money!

Condensing Expressions: 400

• Question: Condense the logarithm to a single quantity.

• Answer

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21[2ln( 3) ln ln( 1)3

x x x

23

2

( 3)1

x xx

Condensing Expressions: 600

• Question:Condense the logarithm to a single quantity. 2[ln x – ln(x + 1) – ln(x – 1)]

• Answer

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2

2 2ln( 1)x

x

Condensing Expressions: 800

• Question: Condense the logarithm to a single quantity.

• Answer

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1[ln 2ln( 4)] ln( 1)3

y y y

23 ( 4)ln

1y yy

Condensing Expressions: 1000

• Question:Condense the logarithm to a single quantity.

• Answer:

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1 [ln( 1) 2ln( 1)] 3ln2

x x x

3ln( ( 1) 1)x x x

Solving Equations: 200

• Question:Solve ln(2x – 1) = 5. Round to the nearest hundredth.

• Answer

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5 1 74.712

e

Solving Equations: 400

• Question:Solve e2x – 4ex – 5 = 0. Round to 3 decimal places.

• Answerln5≈1.609

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Solving Equations: 600

• Question:Solve -2 + 2ln(3x) = 17. Round to 3 decimal places.

• Answer4453.242

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Solving Equations: 800

• Question:Solve ln(x + 5) = ln(x – 1) – ln (x + 1)

• AnswerNo real solution.

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Solving Equations: 1000

• Question: Solve and round to 3 decimal places.

• Answer180.384

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log8 log(1 ) 2x x